UA ALM 20260210

1. Introduction

Brennen Slaney

Personal Background

  • Grew up in Cincinnati, OH
  • Family is from Pittsburgh, huge Steelers fan
  • Have lived in Nashville, TN since graduating
  • Love to travel, run, lift, catch up with friends and try new restuarants

Education

  • Attended the University of Alabama from 2016-2019
  • Bachelors in Finance
  • Masters in Applied Statistics

Career

Cigna

  • Started off as a health actuary in Cigna’s Nashville office as a part of the Actuarial Executive Development Program
Medicare Pricing
  • Lots of excel based models that broke easily
  • Long hours, all plans for the year were due first Monday in June, very stressful
  • Learned a lot about Excel, VBA and how government funded health insurance worked
Pharmacy Trend
  • Various tools (Excel, R, SQL, Python) and business partners (formulary, FP&A, pricing, underwriting, clinical)
  • Learned how complicated the Rx ecosystem was, many layers and no pricing was straightforward
  • Responsible for a lot of actuarial-judgment on current events, like projecting GLP-1 drug trends in early 2023, or modeling out what financials would be when the COVID emergency status ended

Fortitude Re

  • After 3 years, switched to Life & Annuity Reinsurance
  • Much more asset exposure, long term products
  • Finished final FSA exam in health, began taking CFA exams to learn the asset side of the business
  • You are not stuck in the sector you start in out of college!!
Experience Studies
  • Intersection of data science and actuarial
  • Used Python and GitHub to build internal package called HEAT to handle repeatable tasks in an Experience Study
  • Reformatted studies to modern technology, and present results to Actuarial leaders to inform assumption updates
Planning & Strategy
  • Learning and applying a lot of the ALM concepts presented today!
  • Run Quarterly SBA ALM Model using inputs from actuarial modeling, investment analytics and capital management. We own the modeling and reinvestment to keep ALM principles in line throughout the projection
  • Produce daily hedge targets using an automated Python script that runs each night to attribute daily changes to different data updates
  • Investments ALM team uses our hedge targets to understand duration and convexity shifts in liabilities overnight, compare to assets, and place swap trades as needed to keep duration within threshold

Credentials

  • ASA in 2022
  • FSA in 2024
  • Passed CFA Levels I and II, taking III in August

2. Building Blocks of ALM

How are assets and liabilities measured, and why do actuaries care?

Assets

Assets are the money you have. Most of it is invested in safe, predictable instruments:

  • Treasuries
  • Highly rated corporate bonds
  • Mortgage-Backed Securities
  • Not much Bitcoin

The goal is positive expected yield with lower variance. Regulators enforce capital requirements and “score” the safety of assets. Investment teams manage the portfolio, but actuaries are often involved.

For this presentation we’ll use the following sample portfolio:

Sample Asset Portfolio
instrument face_value coupon_rate maturity
$15M UST 1Y $15,000,000 3.68% 1
$10M UST 1Y $10,000,000 3.49% 1
$25M UST 7Y $25,000,000 3.98% 7
$15M Corp A 5Y $15,000,000 4.25% 5
$10M PC BB 20Y $10,000,000 10.50% 20

Liabilities

Liabilities are money you owe. Nearly every insurance contract comes with a liability for the insurer. The timing and amount can be known or unknown:

  • Known — Annuity Certain (fixed schedule of payments)
  • Unknown — Term Life (death benefit contingent on mortality)

Actuaries are the liability experts!

Liability Summary
product amount amount_label premium premium_label age
Whole Life $1,000,000 face value $9,730 annual 40
SPIA $120,000 annual payout $1,734,014 single 65

Equity

Equity = Assets - Liabilities

  • Without equity, a company will be liquidated by regulators
  • Stability is important — you don’t want drastic swings
  • Excess capital funds expansion, retained earnings, and dividends
  • When you buy a stock, you are taking a stake in their equity. $0 Equity = $0 Stock Price
Example

If Assets = $100M and Liabilities = $80M, then Equity = $20M. That $20M funds new projects, dividends, bonuses, regulatory requirements.

3. Cashflows from Assets and Liabilities

What do these things actually look like?

Asset Cashflows

$25M UST 7Y — Cashflows (first 10 periods)
period coupon principal total
1 $497,500 $0 $497,500
2 $497,500 $0 $497,500
3 $497,500 $0 $497,500
4 $497,500 $0 $497,500
5 $497,500 $0 $497,500
6 $497,500 $0 $497,500
7 $497,500 $0 $497,500
8 $497,500 $0 $497,500
9 $497,500 $0 $497,500
10 $497,500 $0 $497,500

Liability Cashflows

Whole Life — Expected Cashflows (first 24 periods)
period year survival_prob expected_premium expected_benefit net_cashflow
1 0.083333 0.9999 $811 $80 −$731
2 0.166667 0.9998 $811 $80 −$731
3 0.25 0.9998 $811 $80 −$731
4 0.333333 0.9997 $811 $80 −$731
5 0.416667 0.9996 $811 $80 −$731
6 0.5 0.9995 $811 $80 −$731
7 0.583333 0.9994 $810 $80 −$731
8 0.666667 0.9994 $810 $80 −$731
9 0.75 0.9993 $810 $80 −$731
10 0.833333 0.9992 $810 $80 −$731
11 0.916667 0.9991 $810 $80 −$731
12 1.0 0.9990 $810 $80 −$731
13 1.083333 0.9990 $810 $86 −$724
14 1.166667 0.9989 $810 $86 −$724
15 1.25 0.9988 $810 $86 −$724
16 1.333333 0.9987 $810 $86 −$724
17 1.416667 0.9986 $810 $86 −$724
18 1.5 0.9985 $810 $86 −$724
19 1.583333 0.9984 $810 $86 −$724
20 1.666667 0.9984 $810 $86 −$724
21 1.75 0.9983 $810 $86 −$724
22 1.833333 0.9982 $809 $86 −$724
23 1.916667 0.9981 $809 $86 −$724
24 2.0 0.9980 $809 $86 −$724
SPIA — Expected Cashflows (first 24 periods)
period year payout survival_prob expected_payout
1 0.083333 $10,000 0.9994 $9,994
2 0.166667 $10,000 0.9989 $9,989
3 0.25 $10,000 0.9983 $9,983
4 0.333333 $10,000 0.9977 $9,977
5 0.416667 $10,000 0.9972 $9,972
6 0.5 $10,000 0.9966 $9,966
7 0.583333 $10,000 0.9960 $9,960
8 0.666667 $10,000 0.9954 $9,954
9 0.75 $10,000 0.9949 $9,949
10 0.833333 $10,000 0.9943 $9,943
11 0.916667 $10,000 0.9937 $9,937
12 1.0 $10,000 0.9932 $9,932
13 1.083333 $10,000 0.9926 $9,926
14 1.166667 $10,000 0.9920 $9,920
15 1.25 $10,000 0.9914 $9,914
16 1.333333 $10,000 0.9908 $9,908
17 1.416667 $10,000 0.9902 $9,902
18 1.5 $10,000 0.9896 $9,896
19 1.583333 $10,000 0.9890 $9,890
20 1.666667 $10,000 0.9884 $9,884
21 1.75 $10,000 0.9877 $9,877
22 1.833333 $10,000 0.9871 $9,871
23 1.916667 $10,000 0.9865 $9,865
24 2.0 $10,000 0.9859 $9,859

Equity (Surplus) View

Balance Sheet — Present Values
component present_value
Assets $83,932,581
Liabilities $1,734,014
Surplus (Equity) $82,198,568

That’s all there is to it — as long as interest rates never change again! Once we confirm that, we can go on a nice vacation and our work is done.

…okay, there’s more work to do.

4. Key Mathematical Concepts

Let’s measure interest rate risk.

Duration

Duration is the time-weighted average of the present value of cashflows. It measures a bond’s sensitivity to interest rate changes and helps us linearly estimate price changes from rate movements.

Convexity

Convexity captures the second-order (curvature) effect of yield changes on price. Using duration and convexity leads to better price-change estimates.

The second-order price approximation is:

DV01 (Dollar Value of a Basis Point)

The dollar change in value for a 1 bps parallel shift in the yield curve. This tells us how much money we expect our portfolio to move from a 1 bps shift.

DV01 by Instrument
instrument dv01
$15M UST 1Y $1,453
$10M UST 1Y $967
$25M UST 7Y $15,122
$15M Corp A 5Y $6,781
$10M PC BB 20Y $21,474

Key Rate Duration (KRD)

The dollar change in value for a 1 bps shift at a specific duration on the yield curve. For example, KRD-7 measures the Dollar-Duration impact of a rate shift ONLY at year 7.

Key properties:

  • KRDs across all tenors sum to the bond’s effective duration
  • A bullet bond has KRD concentrated at its maturity
  • An amortizing bond (e.g. mortgage) has KRD spread across many tenors

Immunization (Preview)

Redington Immunization Conditions

Immunization protects a portfolio’s ability to meet liabilities against interest rate movements:

  1. PV Match: PV(Assets) = PV(Liabilities)
  2. Duration Match: Duration(Assets) = Duration(Liabilities)
  3. Convexity Condition: Convexity(Assets) >= Convexity(Liabilities)

5. Revisit Cashflows with Rate Shocks

What happens when interest rates move?

Present Values Under Rate Shocks
rate_shock discount_rate pv_assets pv_liabilities surplus
-1% 3.0% $88,767,255 $1,988,116 $86,779,140
+0% 4.0% $83,932,581 $1,734,014 $82,198,568
+1% 5.0% $79,584,033 $1,533,753 $78,050,280
+2% 6.0% $75,655,892 $1,372,436 $74,283,456
Key Observation

Notice how assets and liabilities respond differently to rate changes. This mismatch is the core problem ALM solves.

6. Duration Hedging with Swaps

Strategic Asset Allocation

Strategic Asset Allocation (SAA) determines how well assets and liabilities naturally hedge each other.

  • Are our liabilities and assets of similar duration and convexity?
  • Are they similarly sensitive to interest rates?
  • If our bonds change in value similarly to our annuities, we have a natural ALM hedge
  • If they respond differently, we need to actively stabilize the surplus
Default SAA Weights
asset_class weight
govt_bonds 40%
corp_bonds 30%
mortgages 20%
private_credit 10%

Interest Rate Swaps

A plain-vanilla interest rate swap exchanges fixed payments for floating payments. Swaps adjust portfolio duration without buying or selling bonds:

  • Receive-fixed adds duration (like buying a bond)
  • Pay-fixed removes duration (like selling a bond)
Swap DV01
swap notional dv01
5Y Receive-Fixed $10,000,000 $4,491
10Y Receive-Fixed $10,000,000 $8,176

Duration Gap Analysis

Duration Gap Analysis
component dv01
Assets $45,797
Liabilities $2,242
Gap (L - A) −$43,555

7. Immunization

Immunization matches both duration and convexity to protect surplus against rate movements.

We solve a 2x2 system using two hedging instruments (e.g. a 5Y and 10Y swap):

where denotes dollar convexity.

Gaps to Close
metric gap
Dollar Duration (DV01) −$43,555
Dollar Convexity −$4,318,446,840
Immunization Hedge Notionals
instrument notional direction
5Y Swap $5,808,930 Receive-fixed
10Y Swap −$56,464,725 Pay-fixed
Surplus: Unhedged vs Immunized
rate_shock surplus_unhedged surplus_hedged
-1% $86,779,140 $82,199,882
+0% $82,198,568 $82,198,568
+1% $78,050,280 $82,197,268
+2% $74,283,456 $82,188,468

8. Conclusion

Key Takeaways
  • Assets must be structured to meet liabilities under multiple rate scenarios
  • Duration and convexity are the primary tools for measuring interest rate risk
  • DV01 translates rate sensitivity into dollar terms at the portfolio level
  • Immunization (matching duration + convexity) protects surplus from rate movements
  • Strategic Asset Allocation and interest rate swaps are practical hedging tools
  • Diversification across asset classes reduces mismatch risk
  • Regular surplus monitoring is essential for actuarial compliance

Key ALM Strategies

Strategy Description
Immunization Match duration and convexity of assets to liabilities to protect surplus
Cash Flow Matching Structure asset cash flows to precisely meet liability payment schedules
Surplus Optimization Maximize expected surplus return subject to risk constraints

Questions & Discussion

Source code: github.com/realslimslaney/ALM